This third volume in Vladimir Tkachuk's series on Cp-theory problems
applies all modern methods of Cp-theory to study compactness-like
properties in function spaces and introduces the reader to the theory of
compact spaces widely used in Functional Analysis. The text is designed
to bring a dedicated reader from basic topological principles to the
frontiers of modern research covering a wide variety of topics in
Cp-theory and general topology at the professional level.
The first volume, Topological and Function Spaces (c) 2011, provided
an introduction from scratch to Cp-theory and general topology,
preparing the reader for a professional understanding of Cp-theory in
the last section of its main text. The second volume, Special Features
of Function Spaces (c) 2014, continued from the first, giving
reasonably complete coverage of Cp-theory, systematically introducing
each of the major topics and providing 500 carefully selected problems
and exercises with complete solutions. This third volume is
self-contained and works in tandem with the other two, containing five
hundred carefully selected problems and solutions. It can also be
considered as an introduction to advanced set theory and descriptive set
theory, presenting diverse topics of the theory of function spaces with
the topology of point wise convergence, or Cp-theory which exists at the
intersection of topological algebra, functional analysis and general
topology.